Cosmology with reconstructions of the Local Universe - from the Wiener filter to neural nets

Reconstructions of the 3D matter density and peculiar velocity fields from the observed distribution of galaxies provide a valuable probe of cosmic structure formation that is complementary to the study of density or velocity correlation functions. They provide constraints on the local growth rate and are crucial to reduce errors on local measurements of the Hubble constant, to name just two applications. In my talk, I will first show results obtained from the 2MASS Redshift Survey, using our publicly available reconstruction code CORAS. It generates constrained field realizations based on the traditional linear Wiener filter estimate, representing the ensemble of possible reconstructions compatible with the noisy observations. Afterwards, I will show how neural networks can be used to further improve the accuracy and versatility of these reconstructions. In particular, I will try to demystify the application of neural networks by explaining their mathematical relation to the Wiener filter and other well-understood statistical estimators.